Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

A functional screen identifies lateral transfer of beta-glucuronidase (gus) from bacteria to fungi

Lateral gene transfer (LGT) from prokaryotes to microbial eukaryotes is usually detected by chance through genome-sequencing projects. Here, we explore a different, hypothesis-driven approach. We show that the fitness advantage associated with the transferred gene, typically invoked only in retrospect, can be used to design a functional screen capable of identifying postulated LGT cases. We hypothesized that beta-glucuronidase (gus) genes may be prone to LGT from bacteria to fungi (thought to lack gus) because this would enable fungi to utilize glucuronides in vertebrate urine as a carbon source. Using an enrichment procedure based on a glucose-releasing glucuronide analog (cellobiouronic acid), we isolated two gus(+) ascomycete fungi from soils (Penicillium canescens and Scopulariopsis sp.). A phylogenetic analysis suggested that their gus genes, as well as the gus genes identified in genomic sequences of the ascomycetes Aspergillus nidulans and Gibberella zeae, had been introgressed laterally from high-GC gram(+) bacteria. Two such bacteria (Arthrobacter spp.), isolated together with the gus(+) fungi, appeared to be the descendants of a bacterial donor organism from which gus had been transferred to fungi. This scenario was independently supported by similar substrate affinities of the encoded beta-glucuronidases, the absence of introns from fungal gus genes, and the similarity between the signal peptide-encoding 5' extensions of some fungal gus genes and the Arthrobacter sequences upstream of gus. Differences in the sequences of the fungal 5' extensions suggested at least two separate introgression events after the divergence of the two main Euascomycete classes. We suggest that deposition of glucuronides on soils as a result of the colonization of land by vertebrates may have favored LGT of gus from bacteria to fungi in soils.